Answer
$| Error| \lt 0.00011$
Work Step by Step
Integrate the integral with respect to $ t $ as follows:
$\int_0^{1} \cos t^2 dt=\int_0^{1} [1-\dfrac{t^2}{2}+\dfrac{t^{8}}{4 !}-...] dx \\=[t-\dfrac{t^5}{10}+\dfrac{t^{9}}{9 \cdot 4 !}-...]_0^{10} ....$
Thus, the error will be calculated as:
$| Error| \lt \dfrac{1}{13 \cdot 6 !} \approx 0.00011$
and $| Error| \lt 0.00011$
